The paper presents bounded volume heat sources and the corresponding functional-analytical expressions for the temperature field. The power density distributions considered here are normal, exponential and parabolic. The sources model real heat sources like the welding arc, laser beam, electron beam, etc., the convection in the weld pool as well as the latent heat due to fusion and solidification. The parameters of the heat source models are unknown a priori and have to be evaluated by solving an inverse heat conduction problem. The functional-analytical technique for calculating 3D temperature fields in butt welding is developed. The proposed technique makes it possible to reduce considerably the total time for data input and solution. It is demonstrated with an example of laser beam welding of steel plates.

This paper presents volume heat sources and the corresponding functional analytical Solutions for the transient temperature field. The considered energy distributions are normal, exponential and parabolic. The method follows the common approach in Computational Welding Mechanics (CWM) to account for the physics of the welding process and the resulting temperature field by phenomenological models for heat conduction. Therefore, the used heat source models are apparent heat sources that incorporate the real heat input as well as the fluid flow in the weld pool and the latent heat connected with phase transformations. The heat source models provide welding characteristics like thermal cycle and Fusion line in the cross section within short computational time. Consequently, inverse techniques on basis of optimisation algorithms enable the adaptation of the models to the experimental data efficiently. Furthermore, the direct evaluation of the energy distribution for the experimental fusion line in the cross section is demonstrated which enhances the numerical optimisation by reducing the number of unknown model Parameters and providing a reasonable initial guess within the model parameter space. The proposed temperature field models are validated with real laser beam welding experiments.